%0 Book Section %1 statphys23_0811 %A Morita, H. %A Kaneko, K. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K bifurcation collective dynamical hamiltonian hopf metastability motion self-excitation statphys23 system topic-3 %T Collective motion in Hamiltonian dynamical systems %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=811 %X A macroscopic system often shows periodic oscillation when far from equilibrium. Such oscillation can be described as a low-dimensional dissipative dynamical system. On the other hand, the system is composed of a number of microscopic elements (molecules, etc.). Considering the system and its environment as a whole system, as in textbooks of equilibrium statistical mechanics, then we can regard the system, at least classically, as a conservative dynamical system with many degrees of freedom. Thus the macroscopic oscillation essentially results from a collective motion out of microscopic high-dimensional chaos. Nevertheless, such a collective motion in a Hamiltonian dynamical system with many degrees of freedom has not been reported thus far. Usually, systems tend to relax to equilibrium within a short time. Although some systems are known not to simply relax but to stay in metastability for a long duration, they do not show macroscopic temporal patterns. Only in dissipative dynamical systems with many degrees of freedom such collective motion have been observed. However, we discover the collective oscillation in some Hamiltonian dynamical systems. On the way of relaxation to equilibrium, the systems are trapped into metastability, where macroscopic variables show periodic motion. Even in the thermodynamic limit, this macroscopic oscillation survives, showing a violation of the law of large numbers, and the lifetime of the metastability diverges. This collective motion appears through Hopf bifurcation, as in low-dimensional dissipative dynamical systems. Moreover, this metastability is stabilized with excitation by the macroscopic oscillation itself, i.e. self-excitation, whereas usual dissipative systems are sustained with external excitation. In the presentation, we discuss the above mechanism in Hamiltonian dynamical systems of mean-field XY model and mean-field $\phi^4$ model, by showing the common properties.

@incollection{statphys23_0811, abstract = {A macroscopic system often shows periodic oscillation when far from equilibrium. Such oscillation can be described as a low-dimensional dissipative dynamical system. On the other hand, the system is composed of a number of microscopic elements (molecules, etc.). Considering the system and its environment as a whole system, as in textbooks of equilibrium statistical mechanics, then we can regard the system, at least classically, as a conservative dynamical system with many degrees of freedom. Thus the macroscopic oscillation essentially results from a collective motion out of microscopic high-dimensional chaos. Nevertheless, such a collective motion in a Hamiltonian dynamical system with many degrees of freedom has not been reported thus far. Usually, systems tend to relax to equilibrium within a short time. Although some systems are known not to simply relax but to stay in metastability for a long duration, they do not show macroscopic temporal patterns. Only in dissipative dynamical systems with many degrees of freedom such collective motion have been observed. However, we discover the collective oscillation in some Hamiltonian dynamical systems. On the way of relaxation to equilibrium, the systems are trapped into metastability, where macroscopic variables show periodic motion. Even in the thermodynamic limit, this macroscopic oscillation survives, showing a violation of the law of large numbers, and the lifetime of the metastability diverges. This collective motion appears through Hopf bifurcation, as in low-dimensional dissipative dynamical systems. Moreover, this metastability is stabilized with excitation by the macroscopic oscillation itself, i.e. self-excitation, whereas usual dissipative systems are sustained with external excitation. In the presentation, we discuss the above mechanism in Hamiltonian dynamical systems of mean-field XY model and mean-field $\phi^4$ model, by showing the common properties.}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Morita, H. and Kaneko, K.}, biburl = {https://www.bibsonomy.org/bibtex/272922e2161277a12aa5b545019de7224/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {c6a0b3756a748a1bfd221d4b0db4a26f}, intrahash = {72922e2161277a12aa5b545019de7224}, keywords = {bifurcation collective dynamical hamiltonian hopf metastability motion self-excitation statphys23 system topic-3}, month = {9-13 July}, timestamp = {2007-06-20T10:16:30.000+0200}, title = {Collective motion in Hamiltonian dynamical systems}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=811}, year = 2007 }